Energy efficient satellite maneuvering

ABSTRACT

Energy efficient satellite maneuvering is described herein. One disclosed example method includes maneuvering a satellite that is in an orbit around a space body so that a principle sensitive axis of the satellite is oriented to an orbit frame plane to reduce gravity gradient torques acting upon the satellite. The orbit frame plane is based on an orbit frame vector.

RELATED APPLICATION

This patent arises as a continuation of U.S. patent application Ser. No.15/728,281, which was filed on Oct. 9, 2017 and which claims priority toU.S. patent application Ser. No. 14/940,811, which was filed on Nov. 13,2015, now granted as U.S. Pat. No. 10,005,568. The foregoing U.S. PatentApplications are hereby incorporated herein by reference in itsentirety.

FIELD OF THE DISCLOSURE

This patent relates generally to satellites and, more particularly, toenergy efficient satellite maneuvering.

BACKGROUND

Space vehicles such as satellites or resident space objects (RSO)typically encounter significant gravity torque (e.g., environmentaltorque, environmental torque disturbances, etc.) following launch duringmaneuvers to a final orbit. Typically, a satellite or resident spaceobject (RSO) orbiting the Earth may be positioned in a parking orinitial orbit (e.g., a first orbit) before performing an initialmaneuver to initiate a transfer orbit (geosynchronous transfer orbit,etc.) to reach a final orbit. The satellite may then perform a finalmaneuver to maintain the final orbit. For example, the satellite maystart from a low earth orbit (LEO) and maneuver through a geosynchronoustransfer orbit (GTO) to reach a final geosynchronous orbit (GEO). Duringthese maneuvers, gravity torque and/or momentum increases of a satellitemay require significant use of thrusters and/or momentum devices.

To counteract this gravity gradient torque and/or momentum, some typicalsatellites utilize reaction wheels that are located within thesesatellites. In particular, a reaction wheel includes a flywheel that mayrotate at different speeds for attitude control of a satellite. However,these reaction wheels require additional payload space and/or weight andmay also require energy to operate. Further, some more recent satellitesemploy deployable solar panels to generate power while such satellitesmove towards a final orbit, thereby increasing a moment of inertia and,thus, greater susceptibility to gravity gradient torques, therebynecessitating use of relatively larger reaction wheels, which, in turn,require more payload space and weight for respective launch vehicles.

SUMMARY

An example method includes maneuvering a satellite that is in an orbitaround a space body so that a principle sensitive axis of the satelliteis oriented to an orbit frame plane to reduce gravity gradient torquesacting upon the satellite. The orbit frame plane is based on an orbitframe vector.

An example apparatus includes a maneuvering device of a satellite, andan orientation controller to cause the maneuvering device to orient aprinciple sensitive axis of the satellite to an orbit frame plane toreduce gravity gradient torques acting upon the satellite.

Another example method includes maneuvering a satellite that is in anorbit around a space body to orient a principle sensitive axis of thesatellite to an orbit frame plane. The orbit frame plane is defined byan orbit frame vector. The example method also includes operating atleast one thruster of the satellite to cause a resultant thrust vectorto be perpendicular to the principle sensitive axis to alter an orbitaldistance of the satellite.

Yet another example method includes maneuvering a satellite orbiting aspace body so that a functional vector of the satellite is within anorbit frame plane defined by an orbital frame vector. The orbital framevector is directed from the satellite towards a center of the spacebody. The example method also includes slewing the satellite about thefunctional vector so that a principle sensitive axis of the satellite isoriented to the orbit frame plane.

An example tangible machine readable medium has instructions storedthereon, which when executed, cause a machine to access or determineinertial characteristics of a satellite orbiting a space body toidentify a principle sensitive axis of the satellite, where thesatellite has an associated functional vector, determine an orbit frameplane using an orbit frame transformation matrix, and determine anattitude of the satellite to orient the principle sensitive axis to thedetermined plane, and to orient the functional vector relative to theprinciple sensitive axis based on a function of the functional vector.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an example satellite in which the examples disclosed hereinmay be implemented.

FIG. 2 is an example orbital pathway diagram of the example satellite ofFIG. 1 moving from an initial orbit to a final orbit via a transferorbit.

FIG. 3 is another example orbital pathway diagram depicting differentmaneuvering zones of an example final orbit.

FIG. 4 illustrates an example orbit orientation in accordance with theteachings of this disclosure to reduce gravity gradient torquesexperienced by the example satellite of FIG. 1.

FIG. 5 is a simplified representation of the example satellite of FIG. 1that illustrates determination of example axes associated with theexample orbit orientation of FIG. 4.

FIG. 6 illustrates example vectors and planes of a first example orbitalraising/lowering thrust maneuver of the example satellite of FIG. 1 inaccordance with the teachings of this disclosure.

FIG. 7 is a simplified representation of the example satellite of FIG. 1that illustrates example directional axes associated with the firstexample orbital raising/lowering thrust maneuver of FIG. 6.

FIG. 8 illustrates example vectors and planes of a second exampleorbital raising/lowering thrust maneuver of the example satellite ofFIG. 1 in accordance with the teachings of this disclosure.

FIG. 9 is a simplified representation of the example satellite of FIG. 1that illustrates example directional axes associated with the secondexample orbital raising/lowering thrust maneuver of FIG. 8.

FIG. 10 is an example satellite energy conservation system that may beused to implement the examples disclosed herein.

FIG. 11 is a flowchart representative of an example method to implementthe examples disclosed herein.

FIG. 12 is a flowchart representative of another example method toimplement the examples disclosed herein.

FIG. 13 is a flowchart representative of yet another example method toimplement the examples disclosed herein.

FIG. 14 is a block diagram of an example processor platform capable ofexecuting machine readable instructions to implement the example methodsof FIGS. 11-13.

Wherever possible, the same reference numbers will be used throughoutthe drawing(s) and accompanying written description to refer to the sameor like parts. The figures are not to scale. Wherever possible, the samereference numbers will be used throughout the drawing(s) andaccompanying written description to refer to the same or like parts.

DETAILED DESCRIPTION

Energy efficient satellite maneuvering is disclosed herein. Typically, asatellite or resident space object (RSO) orbiting the Earth may bepositioned in a parking or initial orbit (e.g., a first orbit) beforeperforming an initial maneuver to initiate a transfer orbit(geosynchronous transfer orbit, etc.) to reach a final orbit. Thesatellite may then perform a final maneuver to maintain the final orbit.For example, the satellite may start from a low earth orbit (LEO) andmaneuver through a geosynchronous transfer orbit (GTO) to reach a finalgeosynchronous orbit (GEO). During such maneuvering, the satellite mayencounter gravity gradient torques and/or increased momentum build-up.Further, even in an established orbit (e.g., a final orbit), thesatellite may encounter gravity gradient torque caused by inertialcharacteristics of the satellite (e.g. during a perigee of an orbit).

During these maneuvers and/or maintenance of an orbit, gravity torqueand/or momentum accumulation of a satellite may require significant useof thrusters or other movement devices and, therefore, depletion offuel/thrust resources (e.g., thrust fuel, stored thrust energy) storedwithin the satellite and/or significant use of reaction wheels tocounteract this gravity torque and/or excess momentum. However, thesereaction wheels often require additional payload space and/or weight andmay also require significant energy to operate during a maneuver orre-orientation of the satellite. Some satellites employ deployable solarpanels, thereby increasing a moment of inertia of the satellite, whichcan necessitate use of even larger reaction wheels and, thus, even morepayload space and weight and/or required energy for operation.

The examples disclosed herein enable more compact and lighter satellitesas a result of energy efficient satellite maneuvering. In particular,more efficient satellite maneuvering allows relatively lighter and morespace efficient movement and/or momentum devices (e.g., more compactthrusters, reaction wheels, momentum storage devices, etc.). Theexamples disclosed herein orient and/or determine an orientation of asatellite so that a sensitive axis of the satellite is oriented (e.g.,aligned) to a determined orbit frame plane to reduce (e.g., minimize)gravity gradient torques. In some examples, a thrust vector of thesatellite is oriented to be perpendicular to a sensitive axis of thesatellite to reduce gravity gradient torques acting on the satelliteduring an orbital raise, for example. This reduction of gravity gradienttorques allows the satellite to be maneuvered (e.g., between orbits orwithin an orbit) with relatively less energy and/or reduced use of thesereaction wheel(s), for example. Thus, the reduced energy requirementsenable the satellite to be significantly more compact and lighter,thereby reducing required payload space for delivery vehicles (e.g.,payload space delivery vehicles, rockets, a space shuttle, etc.).

As used herein, the term “satellite” may refer to an RSO and vice-versa.As used herein, the term “satellite” refers to an object orbiting aplanet or other object in space. As used herein, the term “sensor data”refers to information from a sensor used to obtain positional knowledgeof a satellite including, but not limited to, time and range,range-rate, azimuth angle, and/or elevation angle, etc. As used herein,the term “principal sensitive axis” refers to an axis of a satellite orspace vehicle in which the gravity gradients can generate the highestamount of torque to the satellite or space vehicle. As used herein, theterm “sensitive axis” refers to an axis or axes of a satellite or aspace vehicle in which gravity gradients can generate a significantamount of torque to the satellite or space vehicle. As used herein, theterm “benign axis” refers to an axis of the satellite or space vehiclein which gravity gradients generate an insignificant amount of torque(e.g., a minimal amount of torque). As used herein, to align/orient avector and/or axis to a plane (e.g., a calculated plane or anothervector), alignment/oriented means within 5 degrees of the plane.However, this range may vary based on the inertial properties of asatellite and/or capabilities of movement/thrust mechanisms of thesatellite.

While the examples disclosed herein are shown related to orbit thrustraising and/or maintaining orbits, the examples disclosed herein may beapplied to other satellite/RSO applications including, but not limitedto, an attitude sensor boresight, an axis of rotation for solar wings,antenna boresights, an actuator vector, or a payload specific vector. Inthese other examples, a functional vector (e.g., a vector of importance)may be accounted for instead of a thrust vector, for example. Thesevectors may be related to operations and/or functions of the satellitethat are not maneuvering related and/or for maintaining an orbit in anenergy-efficient manner.

FIG. 1 is an example satellite 100 in which the examples disclosedherein may be implemented. The satellite 100 of the illustrated exampleincludes a satellite body 102, which includes on-board processors,batteries and/or fuel tanks, antennae (e.g., communication antennae,etc.) 104, solar panels 106 and a propulsion system 108. The examplepropulsion system 108 includes thrusters 110 that have thrust cones 112.In this example, the solar panels 106 are in a deployed state (e.g.,unfolded away from the satellite body 102), thereby altering theinertial/mass characteristics of the satellite 100 in contrast to anun-deployed state of the satellite 100 where the solar panels 106 arefolded inward towards the satellite body 102.

In operation, the satellite 100 may communicate with external systems(e.g., transmit as well as receive) via the antennae 104 to maneuver thesatellite 100 between orbital paths and/or orbital heights and/or toprovide data to external ground-based systems, for example. Inparticular, the satellite 100 of the illustrated example is maneuveredby activating (e.g., firing) the thrusters 110, which are electric(e.g., ion based, an ion propulsion system, xenon based thrusters,etc.). For example, the satellite 100 may vary a duration and/or pulseof different thrusters of the thrusters 110 to maneuver the satellite100 and/or control an attitude of the example satellite 100 relative toa space body that the satellite orbits.

In the example of FIG. 1, a maneuvering frame of reference 120 of theexample satellite 100 is shown. The maneuvering frame of reference 120illustrates a thruster plume angle 122 that is depicted by the symbol,θ′, a cant angle 124 that is depicted by the symbol, θ, and a slew angle126 that is depicted by the symbol, α. The frame of reference 120depicts numerous degrees of rotational movement in which the satellite100 may be oriented/rotated during an orbit or a movement betweendifferent orbits. In this example, a resultant vector 128 of thesatellite 100 is shown. In particular, the example resultant vector 128depicts a resulting direction of motion of the satellite 100 based onthe vector sum of the activation and/or orientation of individualthrusters of the thrusters 110.

The examples disclosed herein allow the satellite 100 to utilize lessenergy and/or fuel to counteract gravity gradient torques and/or excessmomentum (e.g., momentum build up). In particular, the examplesdisclosed herein enable energy efficient orbital transfers, orbitmaintenance and/or re-orientation of the satellite 100. The resultingenergy savings allows the example satellite 100 to be significantlysmaller due to lower energy requirements and/or fewer requiredmaneuvering components.

FIG. 2 is an example orbital pathway diagram 200 of the examplesatellite 100 of FIG. 1 moving from an initial orbit 202 to a finalorbit 204 via a transfer orbit 206. In the illustrated example of FIG.2, the satellite 100 orbits a space body or planet (e.g., Earth, Mars,etc.) 208 in the initial orbit 202 and is proceeding to the final orbit204. In this example, the satellite 100 begins its travel along thetransfer orbit 206 by performing an initial maneuver using the thrusters110. As the satellite 100 moves from the initial orbit 202 to the finalorbit 204, the satellite 100 moves along a path defined by the transferorbit 206 and uses the thrusters 110 to perform a final maneuver toremain in the final orbit 204. While the example shown in the orbitalpathway diagram 200 depicts the satellite 100 moving from the lowerinitial orbit 202 to the higher final orbit 204, in some examples, thesatellite 100 does not complete the final maneuver to move into thehigher final orbit 204, thereby causing the satellite 100 to orbit alongthe transfer orbit 206. Alternatively, the satellite 100 may proceedfrom the final orbit 204 to the lower/initial orbit 202.

FIG. 3 is another example orbital pathway diagram 300 depictingdifferent maneuvering zones of an example final orbit/orbital pathway301. In the illustrated example of FIG. 3, the satellite 100 is movingalong the example orbit path 301, which includes an unconstrainedattitude region 302 that is characterized by an orbit apogee (e.g., thegreatest distance between the satellite 100 and the planet 208) 304 inwhich the satellite 100 encounters the least amount of gravitationalgradients from the planet 208. The example orbit path 301 also includesa zone 306 in which the satellite 100 may be maneuvered (e.g., slewed)to an attitude in accordance with the teachings of this disclosure toavoid gravity gradient torque from the planet 208, and a zone 308 wheregravity gradients from the planet 208 are avoided by maintaining aconstrained attitude of the satellite 100. In this example, the zone 308is characterized by an orbital perigee 309, in which the planet 208exhibits the greatest amount of gravity gradients on the satellite 100due to the satellite 100 being at the closest proximity (e.g., closestpoint) to the planet 208 in the example orbital path 301.

In the example of FIG. 3, the satellite 100 is slewed to anunconstrained attitude (e.g., the attitude/orientation of the satellite100 is not maintained) in the region 310 of the orbital pathway 301. Inthis example, the orbital pathway 301 also includes an unconstrainedattitude region 312 prior to the satellite 100 moving to the orbitapogee 304. The examples disclosed herein may be applied to transferorbits (e.g., orbital raising) such as those shown in FIG. 2 as well asmaintained orbits such as the example of FIG. 3.

FIG. 4 illustrates an example orbit orientation in accordance with theteachings of this disclosure to reduce gravity gradient torquesexperienced by the example satellite 100 of FIG. 1. In particular, theexample orientation and/or corresponding maneuver (e.g., maneuver tomaintain the example orientation) of the satellite 100 is performed bydefining an attitude (e.g., relative orientation) of the satellite 100that can be maintained to reduce (e.g., minimize) gravity gradienttorques encountered by the satellite 100 from the planet 208 as thesatellite 100 maintains an orbit around the planet 208.

In the illustrated example of FIG. 4, the satellite 100 is orbiting theplanet 208, thereby defining an orbital frame vector 402, which isdenoted by the symbol, O₃, with a corresponding orbital frame plane 404,which is denoted as an O₃ plane. In this example, the vector 402 isdefined from the center of gravity of the planet 208 to the center ofgravity of the satellite 100. Based on the vector 402, the plane 404 isdefined at the center of gravity of the satellite 100 and, also,perpendicular to the vector 402. In the example of FIG. 4, coordinatesystem axes 406 of the plane 404 are shown. In this example, sensitiveprinciple axes 408, 409 of the satellite 100 are shown relative to thevector 402 and the plane 404. In this example, the sensitive axis 408 isthe principle sensitive axis of the satellite 100.

In the example of FIG. 4, to avoid and/or reduce gravity gradient torqueeffects on the satellite 100, the principle sensitive axis 408 and/or atleast one of the sensitive axes of the satellite 100 is placed withinthe plane 404. The determination and/or definition of a sensitiveprinciple axis and/or any of the sensitive principle axes may bedetermined/defined using corresponding example calculations related toorientation/alignment/attitude of the satellite 100 as described indetail below in connection with FIG. 5. However, the exampledefinitions, calculations and/or determinations described below are notexhaustive.

Additionally or alternatively, the example orientation/attitude shown inFIG. 4 may be used to switch orbits and/or orbital heights, for example.In particular, it can be advantageous to provide and/or direct thrustfrom the satellite 100 with minimal and/or substantially zero gravitygradient torque acting upon the satellite 100 during an orbital raise,for example. Alternatively, the sensitive axis 409 is the principlesensitive axis and, accordingly, gravity gradient torque can be reduced(e.g., minimized) by orienting (e.g., aligning) the sensitive axis 409along either the orbital frame vector 402 or the orbital frame plane404, for example.

FIG. 5 is a simplified representation of the example satellite 100 ofFIG. 1 that illustrates determination of example axes corresponding tothe example orbit orientation of FIG. 4 to reduce (e.g., minimize)gravity gradient torque acting upon the satellite 100. In particular,gravity gradient torques encountered by the satellite 100 are reducedand/or minimized based on the mass/inertial characterizations of thesatellite 100 in combination with attitude control described above inconnection with FIG. 4.

To reduce gravity gradient torques encountered by the satellite 100, themass and/or inertial characteristics and experienced gravity gradienttorque of the example satellite 100 are first determined and/orcharacterized, for example. In particular, the satellite 100 ischaracterized as discrete/discretized mass elements 502 at relativedistances from a center of gravity 503 of the satellite 100. Therefore,the spatially dependent inertial characteristics of the satellite 100may depend on whether the satellite 100 is in a deployed or un-deployedstate (e.g., whether the solar panels 106 are deployed from thesatellite body 102). In particular, the mass elements 502, which aredenoted by i, i+1, etc. in this example, may be at varying distancesfrom the center of gravity 503 and, thus, vary the overall inertialcharacteristics of the satellite 100. In this example, the mass/inertialcharacteristics of the mass elements 502 are used to define inertiatensor, I, and/or a mass/inertia matrix and/or for determiningprinciple, sensitive and/or benign axes of the satellite 100. In thisexample, the inertia tensor, I, is a multivariable array defininginertial characteristics of the satellite 100 in directions, x, y and zshown in FIG. 5.

In the example of FIG. 5, based on the inertial properties of thesatellite 100, a gravity gradient torque acting on the satellite 100 iscalculated by Equation 1:

$\begin{matrix}{{\left\lbrack {\overset{\rightarrow}{\tau}}_{\mathcal{g}\mathcal{g}} \right\rbrack^{B\;\prime} = {3\frac{GM}{r^{3}}{\overset{\rightarrow}{O}}_{3} \times I^{B}{\overset{\rightarrow}{O}}_{3}}},} & (1)\end{matrix}$where {right arrow over (τ)}_(gg) is the torque related to gravitygradients (in the satellite 100 body frame), where GM is thegravitational constant of the planet 208, where r is a distance betweenan inertial frame center for the planet 208 (e.g., a mass center of theplanet 208) to the center of gravity of the satellite 100, where {rightarrow over (O)}₃ is a vector (e.g., the vector 402) defined based on anaxis 3, which is based on a third column of the body frame array, thatextends from the center gravity of the satellite 100 to the inertialframe center (e.g., the geometric center and/or the center of gravity)of the planet 208, and where I is the inertia tensor of the satellite100. In this example, the {right arrow over (O)}₃ vector is used toadjust a body frame (e.g., a body reference frame of the satellite 100)to an orbit frame based on the planet 208.

To calculate sensitive principle axes of the satellite 100, Equations 2and 3 below are assumed notation in this calculation:

$\begin{matrix}{{{T^{B\;\prime\; B}I^{B}} = {I^{B\;\prime} = \begin{bmatrix}I_{X} & 0 & 0 \\0 & I_{Y} & 0 \\0 & 0 & I_{Z}\end{bmatrix}}},} & (2) \\{{O_{3} = \begin{bmatrix}T_{13} \\T_{23} \\T_{33}\end{bmatrix}},} & (3)\end{matrix}$where I^(B′) is the principle inertia tensor, T^(B′B) is thetransformation from a geometric body frame to the principle axis at thecenter of gravity of the satellite 100, and O₃ is the third column theaforementioned body frame array of the satellite 100 with respect to theorbit frame, T^(BO) that represents a vector from the center of gravityof the satellite 100 to the center of gravity of the planet 208. Basedon the notations of equations (2) and (3), to calculate the torqueexperienced by the example satellite 100 in the principle axis of theexample satellite 100, a cross product of O₃ and I^(B′) O₃ is taken, asexpressed below by Equation 4:

$\begin{matrix}{{\left\lbrack {\overset{\rightarrow}{\tau}}_{\mathcal{g}\mathcal{g}} \right\rbrack^{B\;\prime} = {{3\frac{GM}{r^{3}}{\overset{\rightarrow}{O}}_{3} \times I^{B^{\prime}}{\overset{\rightarrow}{O}}_{3}} = {3{\frac{GM}{r^{3}}\begin{bmatrix}{T_{23}T_{33}} & \left( {I_{Z} - I_{Y}} \right) \\{T_{13}T_{33}} & \left( {I_{X} - I_{Z}} \right) \\{T_{13}T_{23}} & \left( {I_{Y} - I_{X}} \right)\end{bmatrix}}}}},} & (4)\end{matrix}$where T^(B′B) can be used to rotate [{right arrow over (τ)}_(gg)]^(B′)back into a geometric body frame, in some examples. As can be seen inEquation 4, torque acting on the example satellite 100 is proportionalto principle inertial differences in different orientations. The mostsignificant principle inertial differences correspond to the mostsensitive principle axes. For example, if I_(X) and I_(Z) are identical,gravity gradient torque in the y principle axis will be zero. In anotherexample, if I_(Y) is significantly less than I_(X) and I_(Z), torqueacting relative to I_(Y) and/or in the y direction will produce thelargest torque, thereby resulting in I_(Y) being the most sensitiveprinciple axis. In the view of FIG. 5, the principle sensitive axis 408of FIG. 4 is shown as well as benign axes 504, 506. The benign axes 504,506 of the illustrated example of FIG. 5 indicates axes in which thesatellite 100 is not sensitive to gravity gradient torques (i.e., notsensitive to a requisite degree, etc.).

In some examples, sensitive and benign axes of a space vehicle aredetermined based on known mass/inertial characteristics of the spacevehicle (e.g., pre-defined based on the design of the space vehicle).For example, mass characteristics of the satellite body 102 and thesolar panels 106 may be known based on a design of the satellite 100.While the satellite 100 of the illustrated example is symmetric alongmultiple axes, an asymmetric mass/inertia distribution of a satellitecan result in numerous sensitive axes. However, in such examples, thereis one sensitive axis that can experience the highest amount of gravitygradient torque and, thus, is designated the sensitive principle axis.While the example calculations of FIG. 5 are used for the determinationsabove, these examples are not exhaustive and any appropriatecalculation(s) and/or calculation methods may be used. Some otherexamples disclosed below in FIGS. 6-9 utilize these example calculationsof sensitive and benign axes to orient thrust vectors and/or functionalvectors to minimize gravity gradient torques.

FIG. 6 illustrates example vectors and planes of FIG. 1 of a firstexample orbital raising thrust maneuver of the example satellite 100 inaccordance with the teachings of this disclosure. In the example of FIG.6, the satellite 100 is transferring from a lower orbit (e.g., the orbit202) to a higher altitude orbit (e.g., the orbit 204) during an orbitalraising process. Alternatively, the satellite 100 may be transferringfrom a higher orbit to a lower orbit.

Similar to the example described above in connection with FIGS. 4 and 5,the orbital frame vector 402 and the orbital frame plane 404 are shown.However, in the example of FIG. 6, a thrust vector (e.g., a resultantthrust vector) 602 of the satellite 100, which corresponds to theorbital raise maneuver away from the planet 208, is shown. In thisexample, the satellite 100 has a principle sensitive axis 604 that iswithin the plane 404, and the thrust vector 602 is perpendicular to theprinciple sensitive axis 604, thereby reducing gravity gradient torquesencountered by the satellite 100 resulting from thrust during thisexample maneuver. As a result, the reduction in gravity gradient torquesreduces an amount of maneuvering necessary from the thrusters 110 and/ormomentum devices of the satellite 100, thereby enabling greatercompactness and/or weight savings of the satellite 100.

In this example, the principle sensitive axis 604 of the satellite 100is calculated using the examples described above in connection withFIGS. 4 and 5. In particular, the principle sensitive axis 604 isdetermined based on the inertial characteristics of the satellite 100.As mentioned above in connection with FIG. 5, differences in inertiavalues amongst different coordinate axes results in significant torqueexperienced by the satellite 100.

During execution of the example thrust maneuver of FIG. 6, gravitygradient torques experienced by the satellite 100 are reduced (e.g.,minimized) based on orientation (e.g., alignment) of the principlesensitive axis 604 to the plane 404 in combination with theperpendicular orientation of the thrust vector 602 to the principlesensitive axis 604. Alternatively, the principle sensitive axis 604 maybe oriented to the vector 402.

Because the thrust vector 602 of the satellite 100 of the illustratedexample is perpendicular to the principle sensitive axis 604, the torqueexperienced by the satellite 100 resulting from thrust, which can becontrolled as a net overall thrust, is minimized, for example. In someexamples, the perpendicularity of the thrust vector 602 to the principlesensitive axis 604 is accomplished by controlling the thrusters 110 sothat the resultant thrust from the thrusters 110 defines the thrustvector 602 that is perpendicular to the sensitive axis 604. In otherwords, the direction of thrust may be controlled by directionalorientation of at least one of the thrusters 110 and/or resultant thrustfrom multiple of the thrusters 110, which may not be necessarilyoriented along the thrust vector 602. As a result of this coordinatedcontrol of the thrusters 110, orienting the thrust vector and/orresultant thrust vector 602 to be relatively close and/or aligned withthe center of gravity of the satellite 100 reduces torque transmitted tothe satellite 100, thereby reducing necessary equipment and/or payloadto counteract the torque that would otherwise be experienced by thesatellite 100 during thrust maneuvers, for example. Further, electricsatellites often require deployed solar panels during a transition to ahigher orbit, which have a larger characteristic resultant gravitygradient torque. However, the examples disclosed herein may be used tocounteract the inertial effects of these deployed states.

The example orientation and/or thrust maneuver of FIG. 6 may be executedduring a transfer orbit, during an entire orbit and/or a portion of anorbit. For example, the attitude control described herein may be usedduring portions of a final orbit (e.g., during when the satellite 100travels close to a perigee of an orbit) around the planet 208. In someexamples, the example thrust maneuver is performed in a space body(e.g., a planet, Earth, Venus, etc.) inertial frame such as an Earthcentered inertial frame (ECI), for example.

While the examples disclosed herein show general orientation alignment(e.g., precise alignment) of principle sensitive axes with orbital frameplanes and/or precise perpendicularity of thrust vectors to principlesensitive axes, complete alignment is not necessary to reduce gravitygradient torques experienced by the satellite 100 in any of the examplesdisclosed herein. As such, to reduce gravity gradient torques, theprinciple sensitive axis 604 can be aligned/oriented to a certain degreeto the plane 404 (e.g., within 5 degrees) or the vector 402 to reducegravity gradient torques. Similarly, the thrust vector 602 can also benormal to the principle sensitive axis 604 within a certain degree(e.g., perpendicular within 5 degrees of the sensitive principle axis604). In other words, the benefits of gravity gradient torque reductionbased on the examples disclosed herein may be seen even without preciseorientation/alignment of the principle sensitive axis 604 and the thrustvector 602. The degree to which a principle sensitive axis is orientedto an orbit frame plane/vector and/or to which a thrust vector is normalto a principle sensitive axis may vary based on properties of asatellite (e.g., inertial properties) and/or a degree to which thesatellite can maneuver (e.g., effectiveness of thrust and/or momentumdevices on the satellite).

FIG. 7 is a simplified representation of the example satellite 100 ofFIG. 1 that illustrates example directional axes associated with thefirst example orbital raising/lowering thrust maneuver of FIG. 6. In theview of FIG. 7, benign principle axes 702, 704 are shown relative to theprinciple sensitive axis 604 of the satellite 100. The benign principleaxes 702, 704 of the illustrated example are axes that are not largelyaffected by gravity gradient torques provided to the satellite 100.However, the sensitive principle axis 604 can be significantly affectedby torques due to the mass distribution of the satellite 100 along they-direction, as indicated by the x, y, z coordinate system shown in FIG.7.

To minimize torque applied to the satellite 100, the thrust vector 602is shown oriented perpendicular to the sensitive principle axis 604. Asmentioned above in connection with FIG. 6, alignment of the thrustvector 602 to the center of gravity of the satellite 100 reduces and/orminimizes the amount of torque applied to the satellite 100 due tothrust by reducing (e.g., minimizing) a distance separation (e.g., adelta, an alignment separation) of the thrust vector 602 to the centerof gravity of the satellite 100.

FIG. 8 illustrates example vectors and planes of the example satellite100 of a second example orbital raising/lowering thrust maneuver inaccordance with the teachings of this disclosure. In contrast to theexample of FIGS. 6 and 7, in this example, as the satellite 100 orbitsthe planet 208, the satellite 100 is not able to generate a thrustvector 802 at an orientation that is perpendicular to a principlesensitive axis 804 of the satellite 100. The inability of the satellite100 to generate a thrust vector that is perpendicular to the principlesensitive axis 804 may be a result of a thruster malfunction (e.g., oneor more thrusters inoperable and/or damaged) or a configuration and/orspatial arrangement of the thrusters 110 that limits directionalcapabilities of a net thrust resulting from the thrusters 110.

In the example of FIG. 8, the satellite 100 is first rotated (e.g.,slewed) so that the thrust vector 802 of the satellite 100 is orientedto the orbital frame plane 404. The satellite 100 is then slewed aboutthe thrust vector 802 until the principle sensitive axis 804 is orientedto the plane 404. As mentioned above, the thrust vector 802 of theillustrated example is not perpendicular to the principle sensitive axis804. However, the gravity gradient torque experienced by the satellite100 is still reduced and/or eliminated.

FIG. 9 is a simplified view of the example satellite 100 of FIG. 1 thatillustrates example direction axes associated with the second exampleorbital raising/lowering thrust maneuver of FIG. 8. As can be seen inthe view of FIG. 9, the satellite 100 in this example includes benignaxes 902 and 904 in relation to the thrust vector 802 and the principlesensitive axis 804. In contrast to the example of FIGS. 6 and 7, thethrust vector 802 is not perpendicular to the principle sensitive axis804.

In the example of FIG. 9, the satellite 100 is slewed (e.g.,continuously slewed) about the thrust vector 802 to maintain the thrustvector 802 within the plane 404 via received sensor data, for example.The example satellite 100 is also slewed (e.g., continuously slewed,periodically slewed, etc.) about the thrust vector 802 to maintain theprinciple sensitive axis 804 and/or a sensitive axis of the satellite100 within the plane 404. In particular, a control algorithm may be usedto slew the satellite 100 based on current or predicted position(s)and/or attitude(s) of the satellite 100 based on the received sensordata.

As mentioned above, the examples disclosed herein may be used for otherapplications besides orbital maintenance or orbital raising/lowering(e.g., altering an orbital range/radius). For example, a functionalvector such as a directed communication vector, a solar panel directedvector, a payload specific vector, or a visual sensor vector may bedirected/oriented in the orbital frame instead of a thrust vector.Dependent on the relevant function, these vectors may be orientedrelative to a sensitive principle axis (e.g., perpendicular) and/orrelative to an orbital frame vector/plane (e.g., parallel or within) tominimize an encountered gravity gradient torque. For example, a payloadspecific vector may be pointed towards a space body while a sensitiveaxis of a satellite may be positioned within an orbital frame plane.Additionally or alternatively, the functional vector is oriented/alignedto the orbital frame plane.

FIG. 10 is an example satellite energy conservation system 1000 that maybe used to implement the examples disclosed herein. The satellite energyconservation system 1000 of the illustrated example, which isimplemented in a satellite (e.g., the satellite 100), has a satelliteguidance system 1002, which includes a thrust controller 1006, anorientation controller 1008 and a sensor interface 1010. The exampleenergy conservation system 1000 also includes communications lines 1016that communicatively couple the guidance system (e.g., a satelliteguidance system) 1002, the thrust controller 1006 and/or the sensorinterface 1010 to the satellite thruster(s) 110 shown in FIG. 1. In thisexample, the guidance system 1002 is also communicatively coupled to theantenna 104 which, in turn, is in communication with a ground-basedcommunication system 1020 of the planet 208 in which the satelliteorbits). In the example of FIG. 10, the guidance system 1002 iscommunicatively coupled to and/or includes a database 1022.

In operation, the sensor interface 1010 determines a position and/orattitude of the example satellite. In particular, the sensor interface1010 determines a position, attitude and/or velocity/acceleration vectorof the satellite based on sensor data and/or received sensor data fromthe ground communication system 1020 of the planet 208.

In this example, the satellite is proceeding to a higher orbit based oncommands received from the ground communication system 1020 at theantenna 104. The orientation controller 1008 of the illustrated exampledetermines an orbital reference frame plane (e.g., the plane 404) basedon a vector (e.g., the vector 402) defined from the satellite to theplanet 208. The orientation controller 1008 of the illustrated examplecalculates a principle sensitive axis of the satellite. In otherexamples, the orientation controller accesses mass/inertia data and/or apre-defined sensitive axis of the satellite from the database 1022. Inyet other examples, the sensitive principle axis is assigned (e.g.,received from, continuously received from, uploaded from) the groundcommunication system 1020. In some examples, the orientation controller1008 of the illustrated example also calculates an attitude shift (e.g.,an attitude delta) of the satellite required to orient the principlesensitive axis of the satellite to the orbital reference frame plane.Additionally or alternatively, the example orientation controller 1008calculates an attitude of the satellite in which the principle sensitiveaxis is oriented to the orbital reference frame plane and a thrustvector of the satellite is perpendicular to the principle sensitive axisto move the satellite into the higher orbit while reducing (e.g.,minimizing) gravity gradient torques acting on the satellite. In someexamples, the orientation controller 1008 is a manually controlledinterface via the ground communication system 1020, for example.

Based on the determined/calculated attitude, the thrust controller 1006controls numerous thrusters of the satellite thrusters 110 to move thesatellite to the determined/calculated attitude determined from theorientation controller 1008. In some examples, the thrust controller1006 controls a thrust pattern of multiple thrusters and/or pulsesmultiple thrusters to define a resultant thrust vector to perform themaneuvers necessary to adjust the satellite to the determined attitude.Additionally or alternatively, the thrust controller 1006 controls amomentum device such as a momentum storage device and/or a reactionwheel to alter the attitude of the satellite.

In some examples, the sensitive axis of the satellite is calculatedbased on current conditions of the satellite, which may include fuelburn and/or changes of the satellite based on a deployed condition ofthe satellite (e.g., whether the solar panels of the satellite havedeployed or are undeployed).

While an example manner of implementing satellite energy conservationsystem 1000 is illustrated in FIG. 10, one or more of the elements,processes and/or devices illustrated in FIG. 10 may be combined,divided, re-arranged, omitted, eliminated and/or implemented in anyother way. Further, the example satellite guidance system 1002, theexample thrust controller 1006, the example orientation controller 1008and/or, more generally, the example satellite energy conservation system1000 of FIG. 10 may be implemented by hardware, software, firmwareand/or any combination of hardware, software and/or firmware. Thus, forexample, any of the example satellite guidance system 1002, the examplethrust controller 1006, the example orientation controller 1008 and/or,more generally, the example satellite energy conservation system 1000could be implemented by one or more analog or digital circuit(s), logiccircuits, programmable processor(s), application specific integratedcircuit(s) (ASIC(s)), programmable logic device(s) (PLD(s)) and/or fieldprogrammable logic device(s) (FPLD(s)). When reading any of theapparatus or system claims of this patent to cover a purely softwareand/or firmware implementation, at least one of the example satelliteguidance system 1002, the example thrust controller 1006, and/or theexample orientation controller 1008 is/are hereby expressly defined toinclude a tangible computer readable storage device or storage disk suchas a memory, a digital versatile disk (DVD), a compact disk (CD), aBlu-ray disk, etc. storing the software and/or firmware. Further still,the example satellite energy conservation system 1000 of FIG. 10 mayinclude one or more elements, processes and/or devices in addition to,or instead of, those illustrated in FIG. 10, and/or may include morethan one of any or all of the illustrated elements, processes anddevices.

Flowcharts representative of example methods for implementing thesatellite energy conservation system 1000 of FIG. 10 are shown in FIGS.11-13. In these examples, the methods may be implemented using machinereadable instructions that comprise a program for execution by aprocessor such as the processor 1412 shown in the example processorplatform 1400 discussed below in connection with FIG. 14. The programmay be embodied in software stored on a tangible computer readablestorage medium such as a CD-ROM, a floppy disk, a hard drive, a digitalversatile disk (DVD), a Blu-ray disk, or a memory associated with theprocessor 1412, but the entire program and/or parts thereof couldalternatively be executed by a device other than the processor 1412and/or embodied in firmware or dedicated hardware. Further, although theexample program is described with reference to the flowchartsillustrated in FIGS. 11-13, many other methods of implementing theexample satellite energy conservation system 1000 may alternatively beused. For example, the order of execution of the blocks may be changed,and/or some of the blocks described may be changed, eliminated, orcombined.

As mentioned above, the example methods of FIGS. 11-13 may beimplemented using coded instructions (e.g., computer and/or machinereadable instructions) stored on a tangible computer readable storagemedium such as a hard disk drive, a flash memory, a read-only memory(ROM), a compact disk (CD), a digital versatile disk (DVD), a cache, arandom-access memory (RAM) and/or any other storage device or storagedisk in which information is stored for any duration (e.g., for extendedtime periods, permanently, for brief instances, for temporarilybuffering, and/or for caching of the information). As used herein, theterm tangible computer readable storage medium is expressly defined toinclude any type of computer readable storage device and/or storage diskand to exclude propagating signals and to exclude transmission media. Asused herein, “tangible computer readable storage medium” and “tangiblemachine readable storage medium” are used interchangeably. Additionallyor alternatively, the example methods of FIGS. 11-13 may be implementedusing coded instructions (e.g., computer and/or machine readableinstructions) stored on a non-transitory computer and/or machinereadable medium such as a hard disk drive, a flash memory, a read-onlymemory, a compact disk, a digital versatile disk, a cache, arandom-access memory and/or any other storage device or storage disk inwhich information is stored for any duration (e.g., for extended timeperiods, permanently, for brief instances, for temporarily buffering,and/or for caching of the information). As used herein, the termnon-transitory computer readable medium is expressly defined to includeany type of computer readable storage device and/or storage disk and toexclude propagating signals and to exclude transmission media. As usedherein, when the phrase “at least” is used as the transition term in apreamble of a claim, it is open-ended in the same manner as the term“comprising” is open ended.

The example method of FIG. 11 begins at block 1100 where a satellitesuch as the satellite 100 is maneuvered and/or oriented to reducegravity gradient torque(s) acting on the satellite from a space body(e.g., the planet 208) (block 1100). In particular, the satellite isorbiting the space body in an orbit (e.g., a final orbit) and may beabout to enter a higher orbit to perform functions (e.g.,communications, information gathering, etc.) at the higher orbit.

In the example of FIG. 11, a position and orientation/attitude of thesatellite is determined (block 1102). For example, a sensor interfacesuch as the sensor interface 1010 may gather and/or collect sensor datato determine the relative position and attitude of the satelliterelative to the space body. In some examples, a predicted velocityand/or attitude of the satellite is determined (e.g., predicted as afunction of time) based on current satellite motion conditions and/orrelative position of the satellite to the space body.

In some examples, the sensitive axis of the satellite is calculated(block 1104). In particular, the mass/inertia data of the satellite maybe used to determine the sensitive axis. In other examples, theprinciple sensitive axis is pre-defined and/or known based on the designof the satellite. Additionally or alternatively, the sensitive axis iscalculated based on updated mass/inertial characteristics thatcorrespond to current conditions of the satellite (e.g., fuel burn,updated conditions of the satellite, etc.).

Next, the satellite of the illustrated example is maneuvered and/ororiented so that a sensitive axis is oriented with a determined orbitalframe plane (e.g., the plane 404) or (block 1106). Alternatively, thesensitive axis is oriented with an orbital frame vector (e.g., thevector 402).

In some examples where the satellite is being moved to a different orbit(e.g., an orbital raising), a thrust vector (e.g., the thrust vector602) of the satellite is oriented perpendicular to the principlesensitive axis (block 1107). In some examples, the thrust vector isoriented perpendicular to the principle sensitive axis simultaneouslywith the sensitive axis of the satellite being oriented to the orbitalframe plane (e.g., during the same maneuver).

In the examples where the satellite is moved to a different orbit, oncethe satellite has been oriented, a thruster or other movement device ofthe satellite is operated/activated to alter an orbital altitude of thesatellite (block 1108). In some examples, this thruster issimultaneously operated for an orbit raising maneuver as the satelliteis being oriented (blocks 1106 and/or 1107) and the process then ends(block 1110). Alternatively, numerous thrusters are activated for aresultant thrust vector that is perpendicular to the principle sensitiveaxis.

FIG. 12 is a flowchart representative of another example method toimplement the examples disclosed herein. In the example method of FIG.12, a satellite orbiting a space body is undergoing an orbital raising,but has limited thrust maneuvering capabilities and/or limited thrusterorientations. The example method of FIG. 12 begins at block 1200 wherethe satellite is initiating an orbital raising maneuver (block 1200).

A first position and a first orientation/attitude of the satellite isdetermined (block 1202). Next, the satellite is maneuvered and/ororiented (e.g., slewed) so that a thrust vector of the satellite iswithin a determined orbital frame plane (e.g., the plane 404) (block1204). For example, the orbital frame plane may be determined as afunction of time by an orientation controller (e.g., the orientationcontroller 1008) of the example satellite. In this example, the orbitalframe plane of the illustrated example is determined as a function ofsatellite position, which changes over time.

In the example of FIG. 12, the satellite is slewed about the thrustvector (e.g., rotated about the thrust vector) so that a sensitive axisof the satellite is oriented to the determined orbital frame plane(block 1206).

After the satellite has been maneuvered, a second position and a secondorientation of the satellite is determined via a sensor interface suchas the sensor interface 1010 (block 1208). In some examples, a groundbased system of the space body determines the position and orientationof the satellite via a communication system such as the groundcommunication system 1020, for example.

Next, it is determined whether further adjustment of the satellite isnecessary (block 1210). In some examples, this determination is made byanalyzing whether continuous attitude adjustment of the satellite isnecessary (e.g., during a portion of an orbit) and/or whether thesatellite has veered away from a planned trajectory.

If it is determined that further adjustment of the satellite isnecessary (block 1210), the process returns control to block 1202. If itis determined that further adjustment of the satellite is not necessary(block 1210), the example process ends (block 1212).

FIG. 13 is a flowchart representative of yet another example method toimplement the examples disclosed herein. The example method begins atblock 1300 where an example satellite orbiting a space body is in afinal orbit (block 1300). However, the satellite is being maneuveredduring portions of the orbit to minimize and/or reduce gravity gradienttorques encountered at the satellite.

In the example of FIG. 13, a first attitude of the satellite isdetermined (block 1302). This determination may occur via communicationwith sensors of a sensor interface (e.g., the sensor interface 1010)and/or ground-based communications (e.g., the communication system1020).

Next, a sensitive axis (e.g., a principle sensitive axis) of thesatellite is determined (block 1303). In some examples, the sensitiveaxis is calculated based on current satellite conditions (e.g., deployedposition, fuel burn, etc.).

In the example of FIG. 13, an orbit frame plane is calculated based onan orbit frame transformation matrix (block 1304). For example, theorbit frame plane may be based on a vector directed from a center ofgravity of the satellite to the center of gravity of the space bodyorbited by the satellite.

In the example of FIG. 13, a second attitude of the satellite isdetermined/calculated to orient the sensitive axis of the satellite tothe orbital frame plane (e.g., the plane 404) (block 1306). For example,an orientation controller such as the orientation controller 1008 maycalculate an attitude change (e.g., delta) for the satellite. In someexamples, the calculated attitude change may be calculated as a functionof time.

Based on the second attitude of the satellite, a thruster and/ormomentum device (e.g., a reaction wheel) of the satellite is controlledby a thrust controller such as the thrust controller 1006 to move thesatellite to the second attitude (block 1307).

Next, it is determined whether further attitude adjustment of thesatellite is necessary (block 1308). If further adjustment of theattitude of the satellite is necessary (block 1308), control of theprocess returns to block 1302. Alternatively, if further adjustment isnot necessary (block 1308), the process ends (block 1310).

FIG. 14 is a block diagram of an example processor platform 1400 capableof executing the example methods of FIGS. 11-13 to implement the examplesatellite energy conservation system 1000 of FIG. 10. The processorplatform 1400 can be, for example, a server, a personal computer, amobile device (e.g., a personal digital assistant (PDA), an Internetappliance, or any other type of computing device.

The processor platform 1400 of the illustrated example includes aprocessor 1412. The processor 1412 of the illustrated example ishardware. For example, the processor 1412 can be implemented by one ormore integrated circuits, logic circuits, microprocessors or controllersfrom any desired family or manufacturer.

The processor 1412 of the illustrated example includes a local memory1413 (e.g., a cache). The example processor 1412 also includes thethrust controller 1005, the orientation controller 1008 and the sensorinterface 1010. The processor 1412 of the illustrated example is incommunication with a main memory including a volatile memory 1414 and anon-volatile memory 1416 via a bus 1418. The volatile memory 1414 may beimplemented by Synchronous Dynamic Random Access Memory (SDRAM), DynamicRandom Access Memory (DRAM), RAMBUS Dynamic Random Access Memory (RDRAM)and/or any other type of random access memory device. The non-volatilememory 1416 may be implemented by flash memory and/or any other desiredtype of memory device. Access to the main memory 1414, 1416 iscontrolled by a memory controller.

The processor platform 1400 of the illustrated example also includes aninterface circuit 1420. The interface circuit 1420 may be implemented byany type of interface standard, such as an Ethernet interface, auniversal serial bus (USB), and/or a PCI express interface.

In the illustrated example, one or more input devices 1422 are connectedto the interface circuit 1420. The input device(s) 1422 permit(s) a userto enter data and commands into the processor 1412. The input device(s)can be implemented by, for example, an audio sensor, a microphone, acamera (still or video), a keyboard, a button, a mouse, a touchscreen, atrack-pad, a trackball, isopoint and/or a voice recognition system.

One or more output devices 1424 are also connected to the interfacecircuit 1420 of the illustrated example. The output devices 1424 can beimplemented, for example, by display devices (e.g., a light emittingdiode (LED), an organic light emitting diode (OLED), a liquid crystaldisplay, a cathode ray tube display (CRT), a touchscreen, a tactileoutput device, a printer and/or speakers). The interface circuit 1420 ofthe illustrated example, thus, typically includes a graphics drivercard, a graphics driver chip or a graphics driver processor.

The interface circuit 1420 of the illustrated example also includes acommunication device such as a transmitter, a receiver, a transceiver, amodem and/or network interface card to facilitate exchange of data withexternal machines (e.g., computing devices of any kind) via a network1426 (e.g., an Ethernet connection, a digital subscriber line (DSL), atelephone line, coaxial cable, a cellular telephone system, etc.).

The processor platform 1400 of the illustrated example also includes oneor more mass storage devices 1428 for storing software and/or data.Examples of such mass storage devices 1428 include floppy disk drives,hard drive disks, compact disk drives, Blu-ray disk drives, RAIDsystems, and digital versatile disk (DVD) drives.

Coded instructions 1432 to implement the methods of FIGS. 11-3 may bestored in the mass storage device 1428, in the volatile memory 1414, inthe non-volatile memory 1416, and/or on a removable tangible computerreadable storage medium such as a CD or DVD.

From the foregoing, it will be appreciated that the above disclosedmethods and apparatus enable energy efficient operations ofsatellites/RSOs, thereby allowing more compact and weight-savingsatellites/RSOs. The increased compactness and weight savings result inreduced payload requirements for corresponding space launch vehicles.

This patent arises as a continuation of U.S. patent application Ser. No.15/728,281, which was filed on Oct. 9, 2017 and which claims priority toU.S. patent application Ser. No. 14/940,811, which was filed on Nov. 13,2015, now granted as U.S. Pat. No. 10,005,568. The foregoing U.S. PatentApplications are hereby incorporated herein by reference in itsentirety.

Although certain example methods and apparatus have been disclosedherein, the scope of coverage of this patent is not limited thereto. Onthe contrary, this patent covers all methods, apparatus and articles ofmanufacture fairly falling within the scope of the claims of thispatent. While satellites are described, the example methods andapparatus may be applied to vehicles, aerodynamic structures, etc.

What is claimed is:
 1. A method comprising: calculating, viainstructions executed by a processor, a sensitive axis of a satellitethat is in an orbit around a space body; and controlling, via a guidancesystem, at least one of a thruster or a reaction wheel to maneuver thesatellite by aligning a functional vector of the satellite to an orbitframe plane and slewing the satellite about the functional vector sothat the sensitive axis is oriented to the orbit frame plane to reducegravity gradient torques acting upon the satellite.
 2. The method asdefined in claim 1, wherein maneuvering the satellite includes rotatingthe satellite about a thrust vector of the satellite.
 3. The method asdefined in claim 1, further including orienting a thrust vector of thesatellite to be perpendicular to the sensitive axis.
 4. The method asdefined in claim 1, wherein calculating the sensitive axis is based onat least one of fuel burned or a deployed condition of the satellite. 5.The method as defined in claim 4, wherein the deployed conditionincludes a degree to which solar panels of the satellite are un-foldedfrom the satellite.
 6. The method as defined in claim 4, furtherincluding detecting, via a sensor, at least one of the fuel burned orthe deployed condition.
 7. The method as defined in claim 1, whereinmaneuvering the satellite further includes accessing a database forinertia data of the satellite, and wherein the sensitive axis iscalculated based on the inertia data.
 8. The method as defined in claim1, wherein the functional vector includes a thrust vector.
 9. Anapparatus comprising: a maneuvering device of a satellite, wherein themaneuvering device includes at least one of a reaction wheel or athruster; and an orientation controller to: calculate a sensitive axisof the satellite, and cause the maneuvering device to orient afunctional vector to be aligned with an orbit frame plane and slew thesatellite about the functional vector to orient the sensitive axis ofthe satellite to the orbit frame plane to reduce gravity gradienttorques acting upon the satellite.
 10. The apparatus as defined in claim9, wherein the orientation controller causes the maneuvering device toorient the functional vector of the satellite with the orbit frameplane.
 11. The apparatus as defined in claim 10, wherein the functionalvector includes a thrust vector.
 12. The apparatus as defined in claim9, wherein the orientation controller calculates the sensitive axis isbased on at least one of fuel burned or a deployed condition of solarpanels of the satellite.
 13. The apparatus as defined in claim 12,further including a sensor to determine the at least one of the fuelburned or the deployed condition.
 14. The apparatus as defined in claim9, wherein the orientation controller causes the thruster to orient athrust vector of the satellite to be perpendicular to the sensitiveaxis.
 15. A non-transitory machine readable medium having instructionsstored thereon, which when executed, cause a processor to: calculate asensitive axis of a satellite orbiting a space body based on sensorreadings of the satellite, the satellite having an associated functionalvector; determine an orbit frame plane using an orbit frametransformation matrix, wherein the orbit frame plane is perpendicular toan orbit frame vector; determine an attitude of the satellite to orientthe sensitive axis to the determined orbit frame plane, and to orientthe functional vector to be aligned with the orbit frame plane; andinstruct a guidance system to direct at least one of a reaction wheel orthruster to move the satellite to the attitude.
 16. The machine readablemedium having instructions stored thereon as defined in claim 15,further cause the processor to maintain an orbital range of thesatellite.
 17. The machine readable medium having instructions storedthereon as defined in claim 15, wherein the functional vector includes athrust vector.
 18. The machine readable medium having instructionsstored thereon as defined in claim 15, wherein the sensitive axis iscalculated based on at least one of fuel burned or a deployed conditionof the satellite.
 19. The machine readable medium having instructionsstored thereon as defined in claim 18, wherein the deployed conditionincludes a degree to which solar panels are un-folded from thesatellite.
 20. The machine readable medium having instructions storedthereon as defined in claim 15, wherein the sensitive axis is calculatedbased on inertia data of the satellite from a database.